The energy levels of the hydrogen atom are given by
[tex]E_n = -13.6 \frac{1}{n^2} [eV][/tex] (1)
where n is the level number. Therefore, the ground state has energy of
[tex]E_1 = -13.6 \frac{1}{1^2} eV = -13.6 eV[/tex]
If the atom absorbs a photon of energy [tex]E=12.09 eV[/tex], the final energy of the hydrogen atom is
[tex]E_f = E_1 + E = -13.6 eV + 12.09 eV =-1.51 eV[/tex]
And we can use eq.(1) to find the corresponding level number:
[tex]n= \sqrt{ \frac{-13.6 eV}{E_f} } = \sqrt{ \frac{-13.6 eV}{-1.51 eV}}= \sqrt{9}=3 [/tex]
So, the electron made a transition to the n=3 level.
